Adaptive multi-window and anti-noise fluctuating commodity sales prediction method

Abstract

The invention discloses an adaptive multi-window and anti-noise fluctuating commodity sales volume prediction method, which comprises the following steps of: (1) constructing a multi-window network architecture, and carrying out parallel processing input through a plurality of sub-networks with different historical window lengths so as to explicitly model a long-short term multi-scale mode in a time sequence; (2) introducing an adaptive multi-window selection mechanism, and dynamically learning an optimal window length matched with the characteristics of the current input sample for each sub-network; and (3) designing a self-adaptive anti-noise module, and injecting anti-noise with variable intensity into the self-adaptive anti-noise module according to the window length of each sub-network so as to enhance the robustness of the model in a high-noise environment. According to the method, through an innovative multi-window network architecture, adaptive window selection and an adaptive anti-noise mechanism, the problems of multi-scale mode modeling and model robustness in a high-fluctuation and high-noise fluctuation commodity sales volume prediction task are effectively solved, and the model prediction accuracy and generalization ability are remarkably improved.

Description

Technical Field

[0001] This invention belongs to the field of artificial intelligence deep learning and time series analysis technology, specifically involving an adaptive multi-window and noise-resistant method for predicting fluctuating commodity sales. Background Technology

[0002] Volatile time series are ubiquitous in the real world, especially in the realm of commodity sales. Accurately predicting the sales trends of volatile commodities (such as blockbuster new products, holiday gift sets, and products influenced by trending events) is crucial for inventory management, logistics scheduling, and marketing decisions. However, such sales series typically exhibit strong non-stationarity, sudden peaks, and high noise, posing significant challenges to forecasting and making it one of the most challenging tasks in the field of time series analysis.

[0003] In recent years, with the rapid development of deep learning technology, a series of models have been applied to time series prediction. For example, Recurrent Neural Networks (RNNs) and their variants, Long Short-Term Memory (LSTM) and Gated Recurrent Units (GRUs), are used to capture temporal dependencies. Subsequently, Convolutional Neural Networks (CNNs) have also been widely adopted due to their advantages in parallel computing and local pattern extraction. In recent years, attention-based models, represented by Transformers (e.g., Informer, Autoformer, FEDformer), have achieved breakthroughs on multiple benchmark datasets thanks to their powerful long-range dependency modeling capabilities. Subsequent works such as PatchTST and iTransformer have further improved performance by refining input representations.

[0004] Despite the significant success of the above model, its performance exhibits the following limitations when directly applied to scenarios involving fluctuating sales sequences: 1. Limitations of Fixed Window Length: Existing models generally follow a fixed paradigm—using a pre-defined, globally uniform historical window length (look-back window) as input. However, the drivers of product sales forecasting are multi-scale. For example, sales sequences may be influenced by the long-term product lifecycle at certain times, requiring a longer historical perspective; while at other times they may be driven by sudden short-term market sentiment (such as live-streaming sales or negative reviews), requiring short-term data support. Therefore, a fixed window cannot universally adapt to this dynamism, causing the model to be unable to simultaneously accommodate both long-term and short-term patterns.

[0005] 2. Overfitting and Poor Generalization under High Noise: Sales data for fluctuating products often contains significant noise and non-stationarity (such as systematic errors). Complex deep models are highly susceptible to overfitting, meaning they excessively fit the noise and specific patterns in the training data instead of learning the underlying real-world patterns. This directly leads to a sharp deterioration in the model's generalization performance in real-world business scenarios. While some regularization techniques (such as Dropout and weight decay) are widely used, they are typically static and fail to address the inherent noise and varying sensitivity of inputs across different time scales.

[0006] Furthermore, the recently emerging Large Language Model (LLM) has also been explored for sales time-series prediction. These methods mostly involve converting numerical sequences into text prompts (prompt-based) or aligning them to the LLM's embedding space through an adapter (embedding-alignment). While LLM demonstrates potential for pattern recognition, it still faces significant challenges in the volatile task of predicting product sales: it lacks explicit multi-scale modeling mechanisms, is highly sensitive to noise, has high inference costs, and its decision-making process is opaque, making it difficult to meet stringent requirements for efficiency, robustness, and interpretability.

[0007] In summary, current technology urgently needs a novel prediction architecture that can dynamically sense and adapt to the multi-scale characteristics of input sequences, while possessing strong noise resistance and generalization robustness. This invention is proposed against this backdrop. Summary of the Invention

[0008] This invention aims to systematically address two core pain points in predicting fluctuating commodity sales: (1) How to break through the limitation of fixed window length so that the model can adaptively integrate the most relevant long-term and short-term historical information according to the current sales dynamics of the product; (2) How to effectively improve the robustness of the model, prevent overfitting, and ensure its stable generalization ability in real scenarios in high-noise and high-fluctuation sequences.

[0009] To address the above problems, this invention proposes an adaptive multi-window and noise-resistant method for predicting fluctuating commodity sales, comprising the following steps: (1) Input a sequence of original sales of a product over the past L days, and construct a multi-window network architecture. This architecture contains N parallel sub-networks. Each sub-network is assigned an initial and different historical window length to extract sub-sequences of different lengths from the input historical sequence for subsequent processing. (2) An adaptive window selection mechanism is introduced for each sub-network in the multi-window network architecture. This mechanism dynamically adjusts the effective historical window length of the sub-network according to the characteristics of the current input sample through a differentiable dynamic mask. (3) Inject adversarial noise into the input of each subnetwork, and adaptively adjust the strength of the injected adversarial noise according to the historical window length of the subnetwork after adaptive adjustment. The longer the historical window length, the greater the corresponding adversarial noise strength. (4) The outputs of each sub-network are weighted and aggregated through a gating network to obtain the future sales trend prediction results.

[0010] Furthermore, the adaptive window selection mechanism specifically includes: (2.1) For the input sequence of the i-th sub-network, calculate an attention weight vector of the same length as the input sequence; (2.2) The attention weight vector is cumulatively summed to generate a monotonically increasing cumulative weight vector; (2.3) Multiply the cumulative weight vector element-wise with a predictability vector to obtain a dynamic mask, wherein the predictability vector is obtained by calculating the autocorrelation function value between each time point of the input sequence and the prediction target point; (2.4) Multiply the dynamic mask element by element with the original input sequence to obtain the input after adaptive window selection.

[0011] Furthermore, the adversarial noise is generated using a fast gradient sign method.

[0012] Furthermore, for historical window lengths respectively and The two subnetworks, and their corresponding adversarial noise strength and The following relationship must be satisfied: .

[0013] Furthermore, each sub-network in the multi-window network architecture is a multilayer perceptron architecture.

[0014] Furthermore, the gated network is processed by the Softmax function after passing through a linear layer to generate weights for weighted aggregation of the outputs of each sub-network.

[0015] Furthermore, the method is applied to the task of predicting the sales trend of fluctuating commodities, and the output is the upward or downward trend of sales in the next n days compared with the current daily sales.

[0016] To achieve the above objectives, the present invention also provides an adaptive multi-window and noise-resistant fluctuating commodity sales forecasting device, comprising one or more processors for implementing the above-described adaptive multi-window and noise-resistant fluctuating commodity sales forecasting method.

[0017] To achieve the above objectives, the present invention also provides an electronic device, including a memory and a processor, wherein the memory is coupled to the processor; wherein the memory is used to store program data, and the processor is used to execute the program data to implement the above-described adaptive multi-window and noise-resistant fluctuating commodity sales prediction method.

[0018] To achieve the above objectives, the present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described adaptive multi-window and noise-resistant fluctuating commodity sales prediction method.

[0019] Compared with the prior art, the present invention has the following significant advantages: (1) Accurately match business needs: In the scenario of fluctuating commodity sales forecasting, it can adaptively select multiple historical windows such as 15 days, 30 days, and 90 days according to the characteristics of the commodity, effectively integrating short-term event response and long-term sales patterns.

[0020] (2) Significantly improved robustness: Through the theoretically guided adaptive anti-noise mechanism, it can still maintain stable prediction on data with a large amount of noise and non-stationarity (such as systematic errors). On the fluctuating commodity dataset, the Acc index is improved by an average of 4.3%–8.1%, and the MCC index is improved by an average of 19.3%–55.2%.

[0021] (3) High inference efficiency: It adopts a lightweight MLP sub-network and supports parallel computing. The time for a single prediction is only milliseconds, which can be embedded in real-time recommendation or inventory early warning systems.

[0022] (4) Easy end-to-end deployment: No additional calibration or post-processing modules are required. It directly outputs a “sales trend” signal that can be interpreted by the business, which facilitates downstream decision-making and simplifies the deployment process. Attached Figure Description

[0023] Figure 1 This is a diagram illustrating the overall architecture of the method of the present invention; Figure 2 This is a schematic diagram of the structure of the device of the present invention; Figure 3 This is a schematic diagram of an electronic device according to the present invention. Detailed Implementation

[0024] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numerals in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present invention. Rather, they are merely examples of apparatuses and methods consistent with some aspects of the invention as detailed in the appended claims.

[0025] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The singular forms “a,” “the,” and “the” used in this invention and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used herein refers to and includes any or all possible combinations of one or more of the associated listed items.

[0026] This invention proposes an end-to-end trainable framework called "Adaptive Multi-Window and Adversarial Noise Network" (AmanNet). This framework effectively addresses the multi-scale pattern modeling and model robustness issues in the task of predicting fluctuating commodity sales with high volatility and noise through an innovative multi-window network architecture, adaptive window selection, and an adaptive adversarial noise mechanism. The core technology of AmanNet consists of the following three synergistic innovative modules: 1. Multi-Window Networks: As the basic architecture, this invention abandons the single input stream design and instead employs N (e.g., N=3) parallel sub-networks. Each sub-network is initialized to process a historical window of a specific length (e.g., 15 days, 30 days, 90 days, etc.). This design allows the model to learn features in parallel at multiple time granularities (such as short-term promotional effects and long-term seasonal trends), laying the foundation for subsequent adaptive fusion.

[0027] 2. Adaptive Multi-Window Selection: This invention proposes a fully differentiable, end-to-end trained dynamic mechanism to replace the simple hyperparameter optimization process. For the input of each sub-network, the mechanism generates a soft mask, which combines key signals such as dynamic attention and predictability. (1) First, the importance weights of each time step of the input sequence are calculated through a lightweight attention module. (2) Then, by accumulating and summing these weights, a monotonically increasing vector is generated, ensuring that the mask is only truncated from the left (the oldest history), which conforms to the causality of time series. (3) Finally, in order to guide the model to focus on those moments that are more relevant to the future target point, the mask is multiplied by a "predictability" vector calculated based on the autocorrelation function (ACF) to highlight the time periods in history that are highly relevant to future sales (such as the same period last year, the previous promotion, etc.). In this way, the model can "focus" on the most valuable historical segments for each sample and each sub-network, realizing sample-level adaptive window selection.

[0028] 3. Adaptive Adversarial Noise: This invention uses adversarial noise regularization techniques to train the model by adding small perturbations (adversarial noise) to the input, making it more robust to input perturbations. A key innovation lies in the fact that while longer windows contain more information, they are also more prone to overfitting to noise patterns, requiring stronger regularization. Therefore, this invention first demonstrates that the strength of adversarial noise is crucial for balancing the out-of-distribution generalization error of subnetworks with different window lengths. It should be positively correlated with the window length L, specifically the relationship is as follows: Secondly, during training, this invention adds adversarial noise with an intensity adaptively adjusted according to this rule to each sub-network, so that the entire model can achieve excellent noise resistance and generalization performance while maintaining high expressive power.

[0029] like Figure 1 The overall architecture is shown below; the leftmost part is the original input sequence; the middle part is the core processing layer, which contains N parallel sub-networks (N=3 in this figure). The input branches of each sub-network contain an "adaptive multi-window selection" module and an "adaptive adversarial noise" module, respectively; to the left of the expert network is a gating network, which receives the outputs of all sub-networks and performs weighted fusion, and then connects to the prediction mapping layer to finally output the future sales trend prediction result.

[0030] The following is combined Figure 1Taking the daily sales forecast of highly volatile commodities as an example, the specific implementation of the present invention will be described in detail.

[0031] Step 1: Data processing and network initialization.

[0032] Given an original sales sequence P containing the sales data of a product over the past L days (L being the length of the input history), where... ) and M covariates V (such as whether there is a promotion, holiday signs, etc.; among which First, assemble it into The input data is then passed through a linear projection layer to map X to a D-dimensional embedding space. Simultaneously, N parallel sub-networks are initialized, each sub-network i corresponding to an initial window length. .

[0033] Step 2: Detailed process of adaptive multi-window selection.

[0034] For the i-th subnetwork in the k-th layer, its corresponding original input is .

[0035] 1. Dynamic attention calculation: ,in These are learnable parameters.

[0036] 2. Monotonic mask generation: Define the lower triangular matrix ,calculate: Since the softmax output is positive, the generated mask is a monotonically increasing vector.

[0037] 3. Predictability Vector Calculation: Before training, the autocorrelation function (ACF) is calculated using the entire training set. For the t-th time step of subnetwork i (distance from the current time is...), ... Its predictability value is , where n is the prediction step size. This forms the vector: .

[0038] 4. Dynamic mask synthesis: .

[0039] 5. Adaptive selection: At this point, the model has completed the adaptive selection of the effective historical window, obtaining the selected effective historical sales sequence.

[0040] Step 3: Adaptive anti-noise response.

[0041] 1. Baseline noise generation: Using the Fast Gradient Sign Method (FGSM), calculate the loss L pairs. gradient Generate counter-perturbations in a unit direction: .

[0042] 2. Intensity-adaptive scaling: Select the longest window. As a benchmark and its corresponding preset noise intensity For the window of the i-th sub-network Its noise intensity is: .

[0043] 3. Construct the final adversarial examples: .

[0044] Step 4: Feature aggregation and final prediction.

[0045] 1. Sub-network feature extraction: for each adversarial example The feature representation is obtained by feeding it into a multi-layer MLP sub-network (with ReLU activation). .

[0046] 2. Gated weighted fusion: All After being concatenated or summed, the data is fed into an introductory control network (linear layer + Softmax) to generate weights. The final characteristics after fusion are: .

[0047] 3. Predicted Output: After K layers of stacking, the final sequence representation is flattened and passed through a linear layer and a sigmoid function to output the probability of sales increasing / decreasing in the next n days. .like If the forecast is positive, sales are predicted to increase; otherwise, they are predicted to decrease. The model is ultimately optimized end-to-end using binary cross-entropy loss (BCE Loss).

[0048] Implementation Examples To comprehensively evaluate the effectiveness, robustness, and computational efficiency of the AmanNet invention in predicting fluctuating commodity sales, a systematic experiment was conducted. The specific settings are as follows: I. Experimental Setup: 1. Dataset: Daily sales data for multiple real, highly volatile products. These sequences all exhibit significant non-stationarity and high noise characteristics.

[0049] 2. Prediction Task: This invention targets a binary classification task, namely, predicting the upward / downward trend of target sales relative to the current value after n days (e.g., 1 day, 7 days, 30 days, etc.).

[0050] 3. Baseline Models: Including more than 10 advanced time series prediction models, such as traditional statistical methods (ARIMA), classic deep learning models (LSTM, GRU), mainstream Transformer variants (FEDformer, PatchTST, iTransformer, etc.) and representative large language model methods (Time-LLM, GPT4TS).

[0051] 4. Evaluation metrics: Accuracy and Matthews Correlation Coefficient (MCC) are used. MCC is insensitive to imbalance between positive and negative samples and can more reliably measure the model's discrimination ability in real business scenarios.

[0052] 5. Implementation details: All models adopt the same training / validation / test split ratio (7:1:2), standardized preprocessing process and hyperparameter tuning strategy to ensure fair comparison and no data leakage.

[0053] II. Experimental Results: 1. On multiple fluctuating commodity prediction datasets, AmanNet significantly outperformed all baseline models across all data. Accuracy improvements ranged from 4.3% to 8.1%, and MCC improvements ranged from 19.3% to 55.2%. For example, in predicting the sales trend of a certain electrical appliance, the accuracy of this invention increased from 54.1% to 62.7% compared to the baseline; the MCC value increased from 0.130 to 0.243. Furthermore, the results from multiple prediction settings, such as 1 day, 7 days, and 30 days, showed consistent trends, indicating that this method has a stable advantage across different prediction spans.

[0054] 2. Ablation experiment: (1) Full AmanNet: 62.7% accuracy; (2) Remove multi-window structure (use only the longest window): 54.1%; (3) Fixed multi-window (no adaptive selection): 55.3%; (4) Remove adversarial noise module: 58.0%; (5) Use fixed strength adversarial noise: 59.8%.

[0055] The results show that the multi-window architecture, adaptive window selection, and adaptive adversarial noise work synergistically, and the adaptive mechanism is the key to performance improvement.

[0056] Efficiency Analysis: For single-batch inference of sequences with fixed input length, AmanNet's average time is only in the milliseconds, far superior to mainstream Transformer and LLM models. Despite employing a multi-branch structure, the factor network is a lightweight MLP and can be executed in parallel, with controllable overall computational overhead, meeting the latency requirements of practical deployments.

[0057] In summary, this invention, through its specific design for the scenario of predicting commodity sales with high volatility and high noise, effectively solves the problem of multi-scale modeling and noise resistance for highly volatile time series, and has clear technical effects and industrial application value.

[0058] Corresponding to the aforementioned embodiments of the adaptive multi-window and noise-resistant fluctuating commodity sales forecasting method, the present invention also provides embodiments of an adaptive multi-window and noise-resistant fluctuating commodity sales forecasting device.

[0059] See Figure 2 The adaptive multi-window and noise-resistant fluctuating commodity sales forecasting device provided in this embodiment of the invention includes one or more processors for implementing the adaptive multi-window and noise-resistant fluctuating commodity sales forecasting method in the above embodiment.

[0060] The embodiments of the adaptive multi-window and noise-resistant fluctuating commodity sales prediction device of the present invention can be applied to any device with data processing capabilities, such as a computer. The device embodiments can be implemented in software, hardware, or a combination of both. Taking software implementation as an example, as a logical device, it is formed by the processor of any data processing device loading the corresponding computer program instructions from non-volatile memory into memory for execution. From a hardware perspective, such as... Figure 2 The diagram shown is a hardware structure diagram of any data processing-capable device, including the adaptive multi-window and noise-resistant fluctuating commodity sales prediction device of the present invention. Except for... Figure 2 In addition to the processor, memory, network interface, and non-volatile memory shown, any data processing device in the embodiment may also include other hardware depending on the actual function of the data processing device, which will not be described in detail here.

[0061] The specific implementation process of the functions and roles of each unit in the above device can be found in the implementation process of the corresponding steps in the above method, and will not be repeated here.

[0062] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to in the description of the method embodiments. The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of the present invention according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0063] Corresponding to the aforementioned embodiments of the adaptive multi-window and noise-resistant fluctuating sales forecasting method, this application also provides an electronic device, including: one or more processors; a memory for storing one or more programs; when the one or more programs are executed by the one or more processors, the one or more processors implement the adaptive multi-window and noise-resistant fluctuating sales forecasting method as described above. Figure 3 The diagram shown illustrates a hardware structure of any data processing device for which the adaptive multi-window and noise-resistant fluctuating commodity sales prediction method provided in this application embodiment is used. (Except for...) Figure 3 In addition to the processor, memory, DMA controller, disk, and non-volatile memory shown, any data processing device in the embodiment may also include other hardware depending on the actual function of the data processing device, which will not be described in detail here.

[0064] Corresponding to the aforementioned embodiments of the adaptive multi-window and noise-resistant fluctuating commodity sales forecasting method, this embodiment of the invention also provides a computer-readable storage medium storing a program thereon, which, when executed by a processor, implements the adaptive multi-window and noise-resistant fluctuating commodity sales forecasting method described in the above embodiments.

[0065] The computer-readable storage medium can be an internal storage unit of any data processing device described in any of the foregoing embodiments, such as a hard disk or memory. The computer-readable storage medium can also be any data processing device, such as a plug-in hard disk, smart media card (SMC), SD card, flash card, etc., equipped on the device. Furthermore, the computer-readable storage medium can include both internal storage units of any data processing device and external storage devices. The computer-readable storage medium is used to store the computer program and other programs and data required by the data processing device, and can also be used to temporarily store data that has been output or will be output.

[0066] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0067] The above embodiments are only used to illustrate the design concept and features of the present invention, and their purpose is to enable those skilled in the art to understand the content of the present invention and implement it accordingly. The protection scope of the present invention is not limited to the above embodiments. Therefore, all equivalent changes or modifications made based on the principles and design ideas disclosed in the present invention are within the protection scope of the present invention.

Claims

1. An adaptive multi-window and noise-resistant method for predicting fluctuating commodity sales, characterized in that, Includes the following steps: (1) Input a sequence of original sales of a product over the past L days, and construct a multi-window network architecture. This architecture contains N parallel sub-networks. Each sub-network is assigned an initial and different historical window length to extract sub-sequences of different lengths from the input historical sequence for subsequent processing. (2) An adaptive window selection mechanism is introduced for each sub-network in the multi-window network architecture. This mechanism dynamically adjusts the effective historical window length of the sub-network according to the characteristics of the current input sample through a differentiable dynamic mask. (3) Inject adversarial noise into the input of each subnetwork, and adaptively adjust the strength of the injected adversarial noise according to the historical window length of the subnetwork after adaptive adjustment. The longer the historical window length, the greater the corresponding adversarial noise strength. (4) The outputs of each sub-network are weighted and aggregated through a gating network to obtain the future sales trend prediction results.

2. The adaptive multi-window and noise-resistant fluctuating commodity sales forecasting method according to claim 1, characterized in that, The adaptive window selection mechanism specifically includes: (2.1) For the input sequence of the i-th sub-network, calculate an attention weight vector of the same length as the input sequence; (2.2) The attention weight vector is cumulatively summed to generate a monotonically increasing cumulative weight vector; (2.3) Multiply the cumulative weight vector element-wise with a predictability vector to obtain a dynamic mask, wherein the predictability vector is obtained by calculating the autocorrelation function value between each time point of the input sequence and the prediction target point; (2.4) Multiply the dynamic mask element by element with the original input sequence to obtain the input after adaptive window selection.

3. The adaptive multi-window and noise-resistant fluctuating commodity sales forecasting method according to claim 1, characterized in that, The adversarial noise is generated using the fast gradient sign method.

4. The adaptive multi-window and noise-resistant fluctuating commodity sales forecasting method according to claim 1, characterized in that, For historical window lengths respectively and The two subnetworks, and their corresponding adversarial noise strength and The following relationship must be satisfied: .

5. The adaptive multi-window and noise-resistant fluctuating commodity sales forecasting method according to claim 1, characterized in that, Each sub-network in the multi-window network architecture is a multi-layer perceptron architecture.

6. The adaptive multi-window and noise-resistant fluctuating commodity sales forecasting method according to claim 1, characterized in that, The gated network is processed by the Softmax function after passing through a linear layer to generate weights for weighted aggregation of the outputs of each sub-network.

7. The adaptive multi-window and noise-resistant fluctuating commodity sales forecasting method according to claim 1, characterized in that, The method is applied to the task of predicting the sales trend of fluctuating commodities, and the output is the upward or downward trend of sales in the next n days compared with the current daily sales.

8. An adaptive multi-window and noise-resistant fluctuating commodity sales forecasting device, characterized in that, It includes one or more processors for implementing the adaptive multi-window and noise-resistant fluctuating commodity sales forecasting method according to any one of claims 1-7.

9. An electronic device comprising a memory and a processor, characterized in that, The memory is coupled to the processor; wherein the memory is used to store program data, and the processor is used to execute the program data to implement the adaptive multi-window and noise-resistant fluctuating commodity sales forecasting method according to any one of claims 1-7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the adaptive multi-window and noise-resistant fluctuating commodity sales forecasting method as described in any one of claims 1-7.

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